Acta mathematica scientia,Series B ›› 2001, Vol. 21 ›› Issue (2): 249-253.

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A CLASS OF QUADRATIC HAMILTONIAN SYSTEMS UNDER QUADRATIC PERTURBATION

 FENG Jian-Wen, CHEN Shi-Hua   

  1. Department of Mathematics, Wuhan University, Wuhan 430072, China
  • Online:2001-04-07 Published:2001-04-07
  • Supported by:

    This work is supported by NNSF of China.

Abstract:

This paper deals with a class of quadratic Hamiltonian systems with quadratic perturbation. We prove that if the first order Melnikov function M1(h)  0 and the second order Melnikov function M2(h)  0, then the origin of the Hamiltonian system with small perturbation is a center.

Key words: Melnikov function, Hamiltonian system, Center

CLC Number: 

  • 34C
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